TY - JOUR
ID - 2711
TI - $G$-Weights and $p$-Local Rank
JO - Journal of Algebra and Related Topics
JA - JART
LA - en
SN - 2345-3931
AU - Manuel Dominguez Wade, P.
AD - Department of
Mathematics, Matanzas University, Matanzas, Cuba
Y1 - 2017
PY - 2017
VL - 5
IS - 2
SP - 1
EP - 12
KW - Radical vertex
KW - $G$-weight
KW - $p$-local rank
DO - 10.22124/jart.2017.2711
N2 - Let $k$ be field of characteristic $p$, andlet $G$ be any finite group with splitting field $k$. Assume that $B$ is a $p$-block of $G$.In this paper, we introduce the notion of radical $B$-chain $C_{B}$, and we show that the $p$-local rank of $B$ is equals the length of $C_{B}$. Moreover, we prove that the vertex of a simple $kG$-module $S$ is radical if and only if it has the same vertex of the unique direct summand, up to isomorphism, of the Sylow permutationmodule whose radical quotient is isomorphic to $S$. Finally, we prove the vertices of certain direct summands of the Sylow permutation module are bounds for the vertices of simple $kG$-modules.
UR - https://jart.guilan.ac.ir/article_2711.html
L1 - https://jart.guilan.ac.ir/article_2711_8f0e0342d1bad2b4ab66eb7767948d0e.pdf
ER -